Question

How did I make a mistake in this first order DE?

Answer 1

dx/dt+7x=Ae^(-t)
dx/dt+dh/dt x=Ae^(-t)
Be^ht dx/dt+Be^ht dh/dt x=Be^ht Ae^(-t)
(d(Be^ht x))/dt=Be^ht Ae^(-t)
Be^ht x=∫BAe^((h-1)t) dt
e^ht x=A(1/(h-1))e^((h-1)t)
x=A(1/(h-1))e^t

7= dh/dt
h=7t

x=A(1/(7t-1))e^t

Answer 2

it would be easier to annalyse if you put it in the equation tool

Answer 3

I feel that my intuition for the integrating factor is incorrect.

Answer 4

\[x'+7x=Ae^{-t}\]\[x'+h' x=Ae^{-t}\]\[Be^{ht} x''+Be^{ht} h' x=Be^{ht} Ae^{-t}\]

Answer 5

\[Be^{ht} x'+Be^{ht} h'x=Be^{ht} Ae^{-t}\]

Answer 6

I think you were right about having the integrating factor wrong, did you check the table

Answer 7

I prefer not to check from tables. I want to know why this is wrong, not what is right.

Answer 8

No! Chain rule failure. T'was not h', was (ht)'=h!

Answer 9

glad you figured it out! I was starting to do it on my paper, Im not good at looking at stuff and seeing what other people did